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A novel causation analysis method of machining defects for five-axis machine tools based on error spatial morphology of S-shaped test piece

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Abstract

In the acceptance process of newly developed five-axis machine tools (FAMTs), it is urgent for machine tool builders to understand the main causes of machining defects on S-shaped test piece. This paper proposes a novel causation analysis method based on error spatial morphology of S-shaped test piece to decouple the key geometric error parameters causing contour errors of test piece. Firstly, based on multi-body system (MBS) theory, tool axis surface error model of a FAMT is set up. In order to eliminate the effect of theoretical error on contour error of S-shaped test piece, the optimized tool path is planned based on the three-point tangential method. Then, the NC instruction is calculated, and error spatial model is established to characterize contour error of the test piece by considering tool setting position. As a basis, error spatial morphologies of test piece are drawn and the relationships between geometric error parameters and error spatial morphologies are analyzed. In order to decouple the key geometric error parameters affecting contour error of test piece, the causation analysis method of local error and global error are presented. After repairing the local and global key error parameters of the test piece obtained from these two analysis methods respectively, the local machining errors are reduced by more than 80%, and the global machining error is not beyond the tolerance. Finally, the cutting experiments of S-shaped test piece on the FAMT XKAS2525 × 60 are implemented. Error detection results of the cutting test piece are basically the same as that shown in error spatial morphologies of test piece, which verifies the correctness of error spatial model for the test piece. After compensating the global key error parameters obtained from the causation analysis method of global error in CNC system, the detection results of re-cutting test piece under the same conditions indicate the test piece has very few points that are not within the tolerance range, and detection results after compensation and global repaired results are almost similar, which verifies the feasibility and correctness of the proposed analysis method. Therefore, it is obvious that the presented method bridges between geometric characteristics of S-shaped test piece, geometric errors of machine tool, and machining defects of test piece and provides a comprehensive error analysis method in the acceptance and performance testing of FAMTs by using the S-shaped test piece. Thus, this study is of great significance for improving the accuracy evaluation method and enhancing the design accuracy of FAMTs.

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Acknowledgements

The authors appreciate the help provided by BEIJING NO.1 MACHINE TOOL CO., LTD, China in the experiment.

Funding

This work is financially supported by Key Scientific Research Project for Henan Province Higher School of China (No. 18A460036) and the National Natural Science Foundation of China (Nos. 51275014 and 11602229).

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Authors and Affiliations

  1. Henan Key Laboratory of Intelligent Manufacturing of Mechanical Equipment, Zhengzhou University of Light Industry, Zhengzhou City, 450002, Henan Province, China

    Qiaohua Wang, Changjun Wu, Guizhong Xie & Liangwen Wang

  2. Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing, 100124, China

    Jinwei Fan

Authors
  1. Qiaohua Wang
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  2. Changjun Wu
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  3. Jinwei Fan
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  4. Guizhong Xie
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  5. Liangwen Wang
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Correspondence to Changjun Wu.

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Appendices

Appendix 1

$$ {\displaystyle \begin{array}{c}{e}_x={\delta}_{\mathrm{x}}(x)+{\delta}_{\mathrm{x}}(y)+{\delta}_{\mathrm{x}}(z)-{\varepsilon}_{\mathrm{z}}(x)y+{\varepsilon}_{\mathrm{y}}(x)z+{\varepsilon}_{\mathrm{y}}(y)z-{\varepsilon}_{\mathrm{x}\mathrm{y}}y+{\varepsilon}_{\mathrm{x}\mathrm{z}}z\\ {}+{\delta}_{\mathrm{x}}(c)\cos (c)-{\varepsilon}_{\mathrm{y}}(b)\sin (c)-{\delta}_{\mathrm{y}}(c)\sin (c)+{\varepsilon}_{\mathrm{y}}(x){q}_{3\mathrm{z}}+{\varepsilon}_{\mathrm{y}}(x){q}_{4\mathrm{z}}\\ {}+{\varepsilon}_{\mathrm{y}}(x){q}_{5\mathrm{z}}+{\varepsilon}_{\mathrm{y}}(x){q}_{6\mathrm{z}}+{\varepsilon}_{\mathrm{y}}(y){q}_{4\mathrm{z}}+{\varepsilon}_{\mathrm{y}}(y){q}_{5\mathrm{z}}+{\varepsilon}_{\mathrm{y}}(y){q}_{6\mathrm{z}}+{\varepsilon}_{\mathrm{y}}(z){q}_{5\mathrm{z}}\\ {}+{\varepsilon}_{\mathrm{y}}(z){q}_{6\mathrm{z}}-{\varepsilon}_{\mathrm{z}}(x){q}_{3\mathrm{y}}-{\varepsilon}_{\mathrm{z}}(x){q}_{4\mathrm{y}}-{\varepsilon}_{\mathrm{z}}(x){q}_{5\mathrm{y}}-{\varepsilon}_{\mathrm{z}}(y){q}_{4\mathrm{y}}-{\varepsilon}_{\mathrm{z}}(y){q}_{5\mathrm{y}}\\ {}-{\varepsilon}_{\mathrm{z}}(z){q}_{5\mathrm{y}}+{\varepsilon}_{\mathrm{x}\mathrm{c}}{q}_{6\mathrm{z}}-{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{4\mathrm{y}}-{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{5\mathrm{y}}+{\varepsilon}_{\mathrm{x}\mathrm{z}}{q}_{5\mathrm{z}}+{\varepsilon}_{\mathrm{x}\mathrm{z}}{q}_{6\mathrm{z}}+{\delta}_{\mathrm{x}}(b)\cos (b)\cos (c)\\ {}+{\delta}_{\mathrm{z}}(b)\cos (c)\sin (b)-l\cos (c)\sin (b)-{\varepsilon}_{\mathrm{y}}(x)l\cos (b)-{\varepsilon}_{\mathrm{y}}(y)l\cos (b)\\ {}-{\varepsilon}_{\mathrm{y}}(z)l\cos (b)-{\varepsilon}_{\mathrm{x}\mathrm{c}}l\cos (b)-{\varepsilon}_{\mathrm{x}\mathrm{z}}l\cos (b)+{\varepsilon}_{\mathrm{y}}(c){q}_{6\mathrm{z}}\cos (c)-{\varepsilon}_{\mathrm{z}}(c){q}_{6\mathrm{y}}\cos (c)\\ {}-{\varepsilon}_{\mathrm{z}}(x){q}_{6\mathrm{y}}\cos (c)-{\varepsilon}_{\mathrm{z}}(y){q}_{6\mathrm{y}}\cos (c)-{\varepsilon}_{\mathrm{z}}(z){q}_{6\mathrm{y}}\cos (c)-{\delta}_{\mathrm{x}}(b){\varepsilon}_{\mathrm{y}}(x)\sin (b)\\ {}-{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{6\mathrm{y}}\cos (c)-{\varepsilon}_{\mathrm{x}}(b)l\sin (c)+{\varepsilon}_{\mathrm{x}}(c){q}_{6\mathrm{z}}\sin (c)-{\varepsilon}_{\mathrm{z}}(c){q}_{6\mathrm{x}}\sin (c)\\ {}-{\varepsilon}_{\mathrm{z}}(x){q}_{6\mathrm{x}}\sin (c)-{\varepsilon}_{\mathrm{z}}(y){q}_{6\mathrm{x}}\sin (c)-{\varepsilon}_{\mathrm{z}}(z){q}_{6\mathrm{x}}\sin (c)-{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{6\mathrm{x}}\sin (c)\\ {}-{\varepsilon}_{\mathrm{y}}(b)l\cos (b)\cos (c)-{\varepsilon}_{\mathrm{y}}(c)l\cos (b)\cos (c)-{\varepsilon}_{\mathrm{x}}(c)l\cos (b)\cos (c)\\ {}-{\varepsilon}_{\mathrm{bz}}l\cos (b)\sin (c)+{\varepsilon}_{\mathrm{z}}(c)l\sin (b)\sin (c)+{\varepsilon}_{\mathrm{z}}(x)l\sin (b)\sin (c)\\ {}+{\varepsilon}_{\mathrm{z}}(y)l\sin (b)\sin (c)+{\varepsilon}_{\mathrm{z}}(z)l\sin (b)\sin (c)+{\varepsilon}_{\mathrm{x}\mathrm{b}}l\sin (b)\sin (c)\\ {}+{\varepsilon}_{\mathrm{x}\mathrm{y}}l\sin (b)\sin (c)\end{array}} $$
$$ {\displaystyle \begin{array}{c}{e}_y={\delta}_{\mathrm{y}}(x)+{\delta}_{\mathrm{y}}(y)+{\delta}_{\mathrm{y}}(z)-{\varepsilon}_{\mathrm{x}}(x)z-{\varepsilon}_{\mathrm{x}}(y)z-{\varepsilon}_{\mathrm{y}\mathrm{z}}z+{\delta}_{\mathrm{y}}(b)\cos (c)\\ {}+{\delta}_{\mathrm{y}}(c)\cos (c)+{\delta}_{\mathrm{x}}(c)\sin (c)-{\varepsilon}_{\mathrm{x}}(x){q}_{3\mathrm{z}}-{\varepsilon}_{\mathrm{x}}(x){q}_{4\mathrm{z}}-{\varepsilon}_{\mathrm{x}}(x){q}_{5\mathrm{z}}\\ {}-{\varepsilon}_{\mathrm{x}}(x){q}_{6\mathrm{z}}-{\varepsilon}_{\mathrm{x}}(y){q}_{4\mathrm{z}}-{\varepsilon}_{\mathrm{x}}(y){q}_{5\mathrm{z}}-{\varepsilon}_{\mathrm{x}}(y){q}_{6\mathrm{z}}-{\varepsilon}_{\mathrm{x}}(z){q}_{5\mathrm{z}}-{\varepsilon}_{\mathrm{x}}(z){q}_{6\mathrm{z}}\\ {}+{\varepsilon}_{\mathrm{z}}(x){q}_{3\mathrm{x}}+{\varepsilon}_{\mathrm{z}}(x){q}_{4\mathrm{x}}+{\varepsilon}_{\mathrm{z}}(x){q}_{5\mathrm{x}}+{\varepsilon}_{\mathrm{z}}(y){q}_{4\mathrm{x}}+{\varepsilon}_{\mathrm{z}}(y){q}_{5\mathrm{x}}+{\varepsilon}_{\mathrm{z}}(z){q}_{5\mathrm{x}}\\ {}+{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{4\mathrm{x}}+{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{5\mathrm{x}}-{\varepsilon}_{\mathrm{y}\mathrm{c}}{q}_{6\mathrm{z}}-{\varepsilon}_{\mathrm{y}\mathrm{z}}{q}_{5\mathrm{z}}-{\varepsilon}_{\mathrm{y}\mathrm{z}}{q}_{6\mathrm{z}}+{\delta}_{\mathrm{x}}(b)\cos (b)\sin (c)\\ {}+{\delta}_{\mathrm{z}}(b)\sin (b)\sin (c)-{\varepsilon}_{\mathrm{x}}(x)l\cos (b)-{\varepsilon}_{\mathrm{x}}(y)l\cos (b)-{\varepsilon}_{\mathrm{x}}(z)l\cos (b)\\ {}+l{\varepsilon}_{\mathrm{x}}(b)\cos (c)-{\varepsilon}_{\mathrm{y}\mathrm{c}}l\cos (b)-{\varepsilon}_{\mathrm{y}\mathrm{z}}l\cos (b)-{\varepsilon}_{\mathrm{x}}(c){q}_{6\mathrm{z}}\cos (c)\\ {}+{\varepsilon}_{\mathrm{z}}(c){q}_{6\mathrm{x}}\cos (c)+{\varepsilon}_{\mathrm{z}}(x){q}_{6\mathrm{x}}\cos (c)+{\varepsilon}_{\mathrm{z}}(y){q}_{6\mathrm{x}}\cos (c)+{\varepsilon}_{\mathrm{z}}(z){q}_{6\mathrm{x}}\cos (c)\\ {}+{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{6\mathrm{x}}\cos (c)+{\varepsilon}_{\mathrm{y}}(c){q}_{6\mathrm{z}}\sin (c)-{\varepsilon}_{\mathrm{z}}(c){q}_{6\mathrm{y}}\sin (c)-{\varepsilon}_{\mathrm{z}}(x){q}_{6\mathrm{y}}\sin (c)\\ {}-{\varepsilon}_{\mathrm{z}}(y){q}_{6\mathrm{y}}\sin (c)-{\varepsilon}_{\mathrm{z}}(z){q}_{6\mathrm{y}}\sin (c)-{\varepsilon}_{\mathrm{x}\mathrm{y}}{q}_{6\mathrm{y}}\sin (c)-{\varepsilon}_{\mathrm{x}}(c)l\cos (b)\cos (c)\\ {}+{\varepsilon}_{\mathrm{bz}}l\cos (b)\cos (c)-{\varepsilon}_{\mathrm{y}}(b)l\cos (b)\sin (c)+{\varepsilon}_{\mathrm{y}}(c)l\cos (b)\sin (c)\\ {}-{\varepsilon}_{\mathrm{z}}(c)l\cos (c)\sin (b)-{\varepsilon}_{\mathrm{z}}(x)l\cos (c)\sin (b)-{\varepsilon}_{\mathrm{z}}(y)l\cos (c)\sin (b)\\ {}-{\varepsilon}_{\mathrm{z}}(z)l\cos (c)\sin (b)-{\varepsilon}_{\mathrm{x}\mathrm{b}}l\cos (c)\sin (b)-{\varepsilon}_{\mathrm{x}\mathrm{y}}l\cos (c)\sin (b)\end{array}} $$
$$ {\displaystyle \begin{array}{c}{e}_z={\delta}_{\mathrm{z}}(c)+{\delta}_{\mathrm{z}}(x)+{\delta}_{\mathrm{z}}(y)+{\delta}_{\mathrm{z}}(z)+{\varepsilon}_{\mathrm{x}}(x)y+{\delta}_{\mathrm{z}}(b)\cos (b)-{\delta}_{\mathrm{x}}(b)\sin (b)\\ {}+{\varepsilon}_{\mathrm{x}}(c){q}_{6\mathrm{y}}+{\varepsilon}_{\mathrm{x}}(x){q}_{3\mathrm{y}}+{\varepsilon}_{\mathrm{x}}(x){q}_{4\mathrm{y}}+{\varepsilon}_{\mathrm{x}}(x){q}_{5\mathrm{y}}+{\varepsilon}_{\mathrm{x}}(y){q}_{4\mathrm{y}}+{\varepsilon}_{\mathrm{x}}(y){q}_{5\mathrm{y}}\\ {}+{\varepsilon}_{\mathrm{x}}(z){q}_{5\mathrm{y}}-{\varepsilon}_{\mathrm{y}}(c){q}_{6\mathrm{x}}-{\varepsilon}_{\mathrm{y}}(x){q}_{3\mathrm{x}}-{\varepsilon}_{\mathrm{y}}(x){q}_{4\mathrm{x}}-{\varepsilon}_{\mathrm{y}}(x){q}_{5\mathrm{x}}-{\varepsilon}_{\mathrm{y}}(y){q}_{4\mathrm{x}}\\ {}-{\varepsilon}_{\mathrm{y}}(y){q}_{5\mathrm{x}}-{\varepsilon}_{\mathrm{y}}(z){q}_{5\mathrm{x}}-{\varepsilon}_{\mathrm{x}\mathrm{z}}{q}_{5\mathrm{x}}+{\varepsilon}_{\mathrm{y}\mathrm{z}}{q}_{5\mathrm{y}}-{\varepsilon}_{\mathrm{y}}(x){q}_{6\mathrm{x}}\cos (c)\\ {}-{\varepsilon}_{\mathrm{y}}(y){q}_{6\mathrm{x}}\cos (c)-{\varepsilon}_{\mathrm{y}}(z){q}_{6\mathrm{x}}\cos (c)-{\varepsilon}_{\mathrm{x}\mathrm{c}}{q}_{6\mathrm{x}}\cos (c)-{\varepsilon}_{\mathrm{x}\mathrm{z}}{q}_{6\mathrm{x}}\cos (c)\\ {}+{\varepsilon}_{\mathrm{y}\mathrm{c}}{q}_{6\mathrm{y}}\cos (c)+{\varepsilon}_{\mathrm{y}}(b)l\sin (b)+{\varepsilon}_{\mathrm{y}}(c)l\sin (b)+{\varepsilon}_{\mathrm{x}}(x){q}_{6\mathrm{x}}\sin (c)\\ {}+{\varepsilon}_{\mathrm{x}}(y){q}_{6\mathrm{x}}\sin (c)+{\varepsilon}_{\mathrm{x}}(z){q}_{6\mathrm{x}}\sin (c)+{\varepsilon}_{\mathrm{y}}(x){q}_{6\mathrm{y}}\sin (c)+{\varepsilon}_{\mathrm{y}}(y){q}_{6\mathrm{y}}\sin (c)\\ {}+{\varepsilon}_{\mathrm{y}}(z){q}_{6\mathrm{y}}\sin (c)+{\varepsilon}_{\mathrm{x}\mathrm{c}}{q}_{6\mathrm{y}}\sin (c)+{\varepsilon}_{\mathrm{x}\mathrm{z}}{q}_{6\mathrm{y}}\sin (c)+{\varepsilon}_{\mathrm{y}\mathrm{c}}{q}_{6\mathrm{x}}\sin (c)\\ {}+{\varepsilon}_{\mathrm{y}\mathrm{z}}{q}_{6\mathrm{x}}\sin (c)+{\varepsilon}_{\mathrm{y}}(x)l\cos (c)\sin (b)+{\varepsilon}_{\mathrm{y}}(y)l\cos (c)\sin (b)\\ {}+{\varepsilon}_{\mathrm{y}}(z)l\cos (c)\sin (b)+{\varepsilon}_{\mathrm{x}\mathrm{c}}l\cos (c)\sin (b)+{\varepsilon}_{\mathrm{x}\mathrm{z}}l\cos (c)\sin (b)\\ {}-{\varepsilon}_{\mathrm{x}}(x)l\sin (b)\sin (c)-{\varepsilon}_{\mathrm{x}}(y)l\sin (b)\sin (c)-{\varepsilon}_{\mathrm{x}}(z)l\sin (b)\sin (c)\\ {}-{\varepsilon}_{\mathrm{y}\mathrm{c}}l\sin (b)\sin (c)-{\varepsilon}_{\mathrm{y}\mathrm{z}}l\sin (b)\sin (c)+{\varepsilon}_{\mathrm{x}}(b){\varepsilon}_{\mathrm{y}}(z){\varepsilon}_{\mathrm{x}\mathrm{b}}l\cos (c)\end{array}} $$

Appendix 2

Table 7 Control points of S-shaped test piece (unit: mm)
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Wang, Q., Wu, C., Fan, J. et al. A novel causation analysis method of machining defects for five-axis machine tools based on error spatial morphology of S-shaped test piece. Int J Adv Manuf Technol 103, 3529–3556 (2019). https://doi.org/10.1007/s00170-019-03777-0

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